{"slug": "energy-based-models", "title": "Energy-Based Models", "summary": "Energy-Based Models (EBMs) score complete candidate outputs with a single learned energy function, where lower energy indicates a better fit, and can define a probability distribution over outputs by exponentiating negative energy and normalizing with the partition function. Unlike autoregressive models, which factorize a distribution into conditional probabilities, and diffusion models, which factorize over progressive noise levels, an EBM requires neither a variable ordering nor a sequence of noise levels, giving it a direct way to represent global dependencies among output variables. The approach's main cost is computational: maximum-likelihood training typically requires repeated sampling from the current model, which can be slow and difficult in high dimensions, according to the source, which also cites the author's PhD thesis, \"Learning Generalizable Systems by Learning Composable Energy Landscapes.", "body_md": "An Energy-Based Model (EBM) evaluates a proposed output for a given input and returns a single number, called its energy. Lower energy indicates a better fit to the input. In a neural EBM, a network learns this scoring function from data. For example, a robot-planning model can score an entire proposed sequence of states and actions, called a trajectory, given a starting state and a goal.\n\nTo make a prediction, we start with an initial guess and repeatedly adjust the proposed output to reduce its energy. For the robot, we change the proposed states and actions while keeping the starting state, goal, and learned network weights fixed. Gradients tell us how small changes to the trajectory affect its energy, so we can use them to guide these updates. This search for an output with the lowest energy is called energy minimization.\n\nThe same energy function can also define a probability distribution over possible outputs. Exponentiating the negative energy gives each output a positive weight, so lower-energy outputs receive larger weights. Dividing by the sum or integral of these weights, called the partition function, normalizes the distribution. A sampling procedure can then generate different plausible outputs according to this distribution.\n\nAn EBM represents a probability distribution through a single energy function over complete outputs. Autoregressive models factorize the distribution into a product of conditional probabilities, each conditioned on the variables generated so far. Diffusion models introduce noisy intermediate states and factorize the generative process into conditional transitions that progressively remove noise. An EBM does not require either a variable ordering or a sequence of noise levels to define its distribution. Because the energy scores all output variables together, it provides a direct way to represent global dependencies among them. This simple representation comes at a computational cost. Maximum-likelihood training typically requires repeated sampling from the current model, which can be slow and difficult in high dimensions.\n\nWe can also evaluate the same candidate with several energy functions. In [robot planning](https://arxiv.org/abs/1909.06878), one energy can assess whether a trajectory follows the robot’s dynamics, meaning how states change under actions, and another can score how close its final state is to a goal. Adding the energies gives a single score for both requirements. We then adjust the trajectory to reduce this total energy. Weights control the balance between the requirements. Changing the goal energy creates a new planning problem without retraining the dynamics model.\n\nMy PhD thesis, [*Learning Generalizable Systems by Learning Composable Energy Landscapes*](https://yilundu.github.io/thesis.pdf), develops this approach: learning reusable energy landscapes from data, then composing and optimizing them at inference time to solve tasks not represented directly in the training set.\n\n \n**Flexible representation** One function scores complete candidate outputs and can define a probability distribution over them.\n\n**Multiple inference procedures** Change a proposed output to reduce its energy, or sample several plausible outputs from the distribution.\n\n**Composition** Add scores for different requirements and search for an output with low total energy.", "url": "https://wpnews.pro/news/energy-based-models", "canonical_source": "https://energy-based-model.github.io/", "published_at": "2026-09-18 22:23:25+00:00", "updated_at": "2026-09-18 22:55:10.920473+00:00", "lang": "en", "topics": ["machine-learning", "ai-research", "robotics"], "entities": ["Energy-Based Model", "partition function", "autoregressive models", "diffusion models", "Learning Generalizable Systems by Learning Composable Energy Landscapes"], "alternates": {"html": "https://wpnews.pro/news/energy-based-models", "markdown": "https://wpnews.pro/news/energy-based-models.md", "text": "https://wpnews.pro/news/energy-based-models.txt", "jsonld": "https://wpnews.pro/news/energy-based-models.jsonld"}}